A couple of weeks ago I was messing about on Twitter at home on a Friday night when a tweet from the Conservative blogger, publisher and talkshow host Iain Dale brought me up short. He was on the train on his way home to Kent, and posted a picture with the caption: "This is the drunk woman opposite me. I think she's about to puke. Disgusting slapper."

I didn't look at the photo and clicked on "unfollow" straightaway so I wouldn't see any more of Dale's tweets. Holding this woman up to ridicule in front of the 26,000 people who follow him was abusing his position, I thought.

The chorus of outrage now commonly known as a "Twitter storm" followed. Within about five minutes angry voices were calling for Dale to be sacked and I switched my computer off.

The next day Dale posted a blog defending his use of the word "slapper" and explained how, as a non-drinker, he is horrified by public drunkenness. But when I rang him up this week he agreed his comment had been "rude and unchivalrous" and suggested there is something about the spontaneous nature of microblogging sites such as Twitter that brings this out.

"Twitter and blogs are full of bile. A lot of people say things on these sites they would never say to your face or on the phone. I think on a blog, people think you have to be quite aggressive or abrasive," he told me.

This idea is not new. For years commentators, and particularly women, have complained about the personal abuse that often passes for debate on the internet. This style seemed to suit Dale, who launched his blog 10 years ago after failing to win selection as a Tory parliamentary candidate.

But more recently he has switched his focus to radio, where he adopts quite a different persona on his LBC evening talkshow. I asked him whether he thinks the gentler and more polite style of radio (with some exceptions) explains why its audience continues to hold up in the face of new media's continuing onslaught.

"I think people who have only ever known me from my blog and then listen to my radio show think, is this the same person? I cover a lot of subjects that traditionally would have been covered by female presenters – how men react to miscarriage, living with an alcoholic. I've built up this audience of people who are prepared to ring me up and tell me these amazingly personal things. I think people have always regarded radio as a quasi-friend."

With an audience of around a million in the London area, LBC remains small compared with the national BBC and commercial stations. This week's quarterly figures, which showed a small drop-off overall from the previous quarter, but still more than 700,000 more radio listeners than at the same time two years ago, again showcased radio's remarkable resilience, a story that has become familiar over the past few years. Nine out of 10 of us listen to radio every week, with the three biggest BBC stations (1, 2 and 4) holding on to audiences above 10 million.

Overall, the BBC retains well over half the total market, with commercial stations including Talksport and Capital also performing well in a difficult advertising market. In the mornings, Radio 4's flagship Today programme is snapping at the heels of Radio 1's Chris Moyles in the same slot.

What is it about radio that has made it so durable, and able to coexist not only through the age of television, but the age of new media too? As social networking giant Facebook prepares to float itself and raise an astonishing £5bn, what has enabled radio to stand its ground?

The licence fee is the obvious first answer. Former Radio 4 controller Mark Damazer, now master of an Oxford college, says that ever since a crisis of confidence at the BBC in the 1990s, when people wondered whether the Radio 4 spectrum should be given over to rolling news and current affairs, backing for the station and for radio more broadly has been solid, and continued throughout the last decade in spite of predictions that its audience would shrink.

"When 5 Live was launched in 1994, Radio 4 was anxious, it looked like a challenge, but what happened was the reverse. It liberated Radio 4, which then didn't have to worry about breaking a story every five minutes."

Audiences may be booming, but the freezing of the licence fee is still a headache for BBC radio. Recent cuts have left many producers complaining of impossible workloads, and following the reprieve granted 6 Music after a public campaign in 2010 (the station has just recorded its largest audience, of 1.5m), a big row over proposed cuts to local stations is in the offing. But while commercial stations believe the BBC exploits an unfair advantage and is overly dominant, the security of the licence fee has undoubtedly enabled the BBC's radio stations to build and retain an enormous and loyal audience.

Another explanation for radio's staying-power is its cheapness. Radio can be made at a fraction of the cost of television, meaning that programme-makers, DJs and entrepreneurs can all have a crack at it. Commercial broadcasters as well as the BBC value it as an incubator for future TV talent. Added to which, radios themselves are cheap, and all over the place: by people's beds, in the bathroom, in the car.

"Despite the fact you think we're a visually saturated culture, there are all sorts of places where you get radio and nothing else. The technology of radio is cheap, simple and idiot-proof, and older listeners in particular are going to be very reluctant to let it go," says Damazer.

But this attachment on the part of consumers to low technology is also problematic. The switch to digital radio is proving much slower and messier than anyone expected. Digital listening stands at just under 30% and the analogue switch-off looks like being postponed for several more years, meaning more expense and inconvenience for broadcasters who must cater to different signals.

Is radio old or new media? The Wikipedia "new media" definition doesn't mention radio at all, perhaps uncertain whether to lump it in with printing presses or mobile apps. Radio has affinities with the current age of mobile gadgets. The wireless beaming broadcasts into the family living room in the 1920s was a forerunner of the wi-fi box streaming internet signals into the 21st-century home.

Podcasts, downloadable audio and websites such as Radioplayer have enabled radio to make a smooth transition to the computer age. It hasn't suffered the existential threat experienced by the music industry. But plenty of challenges remain, chief among them attracting younger listeners and persuading them to choose DJs rather than making their own playlists on their iPods, or streaming music through Spotify.

Journalists working in talk radio proudly point out that they were talking and listening to members of the public via on-air phone-ins long before newspapers and television began worrying about "mutualisation" and "open-sourcing" of content. James O'Brien, host of another LBC talkshow, says that while he would welcome a change to the broadcasting rules so that opinionated news shows such as his were allowed on TV, he would miss the intimacy of radio. "Television is more declamatory. It's as if you're addressing an audience rather than an individual, and it's the same with a newspaper column, which I think is the closest print equivalent to what I do.

"The image I always have in my head before my show is that I'm getting into the passenger seat of your car, and ideally I'm not going to get on your nerves enough in the next three hours for you to throw me out."

There is a confidence among many of those who work in radio that what they do will carry on. We remain attached to radio and its rhythms, to the hum and the sound of it. And we get attached to the people who present it, when we don't violently take against them. Radio is personal.

Media historian David Hendy says: "The thing about radio is that it's very clever at popping up in new spaces. In America there are groups of people who get together to listen to a programme, like a book group."

Hendy suggests that radio's sense of its own past will serve it well. Last weekend's opening up of the archive of 70 years of Desert Island Discs is a good example. But more than the richness of its back catalogue, or the new technologies that will make it ever more accessible, he believes that what is unique about radio is the place it accords to the human voice. "I think there is a deep, natural, human desire to be accompanied by sound, whether music or voices. It stops us from feeling alone. Radio has intrinsic qualities that give it a good chance of surviving."